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Definition df-at 22748
Description: Define the set of atoms in a Hilbert lattice. An atom is a nonzero element of a lattice such that anything less than it is zero, i.e. it is a smallest nonzero element of the lattice. Definition of atom in [Kalmbach] p. 15. See ela 22749 and elat2 22750 for membership relations. (Contributed by NM, 14-Aug-2002.) (New usage is discouraged.)
Assertion
Ref Expression
df-at  |- HAtoms  =  {
x  e.  CH  |  0H  <oH  x }

Detailed syntax breakdown of Definition df-at
StepHypRef Expression
1 cat 21375 . 2  class HAtoms
2 c0h 21345 . . . 4  class  0H
3 vx . . . . 5  set  x
43cv 1618 . . . 4  class  x
5 ccv 21374 . . . 4  class  <oH
62, 4, 5wbr 3920 . . 3  wff  0H  <oH  x
7 cch 21339 . . 3  class  CH
86, 3, 7crab 2512 . 2  class  { x  e.  CH  |  0H  <oH  x }
91, 8wceq 1619 1  wff HAtoms  =  {
x  e.  CH  |  0H  <oH  x }
Colors of variables: wff set class
This definition is referenced by:  ela  22749  atssch  22753
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